Polytope of Type {4,204}

Play with this polytope as a twisty puzzle

s0 := (  1,207)(  2,208)(  3,205)(  4,206)(  5,211)(  6,212)(  7,209)(  8,210)(  9,215)( 10,216)( 11,213)( 12,214)( 13,219)( 14,220)( 15,217)( 16,218)( 17,223)( 18,224)( 19,221)( 20,222)( 21,227)( 22,228)( 23,225)( 24,226)( 25,231)( 26,232)( 27,229)( 28,230)( 29,235)( 30,236)( 31,233)( 32,234)( 33,239)( 34,240)( 35,237)( 36,238)( 37,243)( 38,244)( 39,241)( 40,242)( 41,247)( 42,248)( 43,245)( 44,246)( 45,251)( 46,252)( 47,249)( 48,250)( 49,255)( 50,256)( 51,253)( 52,254)( 53,259)( 54,260)( 55,257)( 56,258)( 57,263)( 58,264)( 59,261)( 60,262)( 61,267)( 62,268)( 63,265)( 64,266)( 65,271)( 66,272)( 67,269)( 68,270)( 69,275)( 70,276)( 71,273)( 72,274)( 73,279)( 74,280)( 75,277)( 76,278)( 77,283)( 78,284)( 79,281)( 80,282)( 81,287)( 82,288)( 83,285)( 84,286)( 85,291)( 86,292)( 87,289)( 88,290)( 89,295)( 90,296)( 91,293)( 92,294)( 93,299)( 94,300)( 95,297)( 96,298)( 97,303)( 98,304)( 99,301)(100,302)(101,307)(102,308)(103,305)(104,306)(105,311)(106,312)(107,309)(108,310)(109,315)(110,316)(111,313)(112,314)(113,319)(114,320)(115,317)(116,318)(117,323)(118,324)(119,321)(120,322)(121,327)(122,328)(123,325)(124,326)(125,331)(126,332)(127,329)(128,330)(129,335)(130,336)(131,333)(132,334)(133,339)(134,340)(135,337)(136,338)(137,343)(138,344)(139,341)(140,342)(141,347)(142,348)(143,345)(144,346)(145,351)(146,352)(147,349)(148,350)(149,355)(150,356)(151,353)(152,354)(153,359)(154,360)(155,357)(156,358)(157,363)(158,364)(159,361)(160,362)(161,367)(162,368)(163,365)(164,366)(165,371)(166,372)(167,369)(168,370)(169,375)(170,376)(171,373)(172,374)(173,379)(174,380)(175,377)(176,378)(177,383)(178,384)(179,381)(180,382)(181,387)(182,388)(183,385)(184,386)(185,391)(186,392)(187,389)(188,390)(189,395)(190,396)(191,393)(192,394)(193,399)(194,400)(195,397)(196,398)(197,403)(198,404)(199,401)(200,402)(201,407)(202,408)(203,405)(204,406)(409,615)(410,616)(411,613)(412,614)(413,619)(414,620)(415,617)(416,618)(417,623)(418,624)(419,621)(420,622)(421,627)(422,628)(423,625)(424,626)(425,631)(426,632)(427,629)(428,630)(429,635)(430,636)(431,633)(432,634)(433,639)(434,640)(435,637)(436,638)(437,643)(438,644)(439,641)(440,642)(441,647)(442,648)(443,645)(444,646)(445,651)(446,652)(447,649)(448,650)(449,655)(450,656)(451,653)(452,654)(453,659)(454,660)(455,657)(456,658)(457,663)(458,664)(459,661)(460,662)(461,667)(462,668)(463,665)(464,666)(465,671)(466,672)(467,669)(468,670)(469,675)(470,676)(471,673)(472,674)(473,679)(474,680)(475,677)(476,678)(477,683)(478,684)(479,681)(480,682)(481,687)(482,688)(483,685)(484,686)(485,691)(486,692)(487,689)(488,690)(489,695)(490,696)(491,693)(492,694)(493,699)(494,700)(495,697)(496,698)(497,703)(498,704)(499,701)(500,702)(501,707)(502,708)(503,705)(504,706)(505,711)(506,712)(507,709)(508,710)(509,715)(510,716)(511,713)(512,714)(513,719)(514,720)(515,717)(516,718)(517,723)(518,724)(519,721)(520,722)(521,727)(522,728)(523,725)(524,726)(525,731)(526,732)(527,729)(528,730)(529,735)(530,736)(531,733)(532,734)(533,739)(534,740)(535,737)(536,738)(537,743)(538,744)(539,741)(540,742)(541,747)(542,748)(543,745)(544,746)(545,751)(546,752)(547,749)(548,750)(549,755)(550,756)(551,753)(552,754)(553,759)(554,760)(555,757)(556,758)(557,763)(558,764)(559,761)(560,762)(561,767)(562,768)(563,765)(564,766)(565,771)(566,772)(567,769)(568,770)(569,775)(570,776)(571,773)(572,774)(573,779)(574,780)(575,777)(576,778)(577,783)(578,784)(579,781)(580,782)(581,787)(582,788)(583,785)(584,786)(585,791)(586,792)(587,789)(588,790)(589,795)(590,796)(591,793)(592,794)(593,799)(594,800)(595,797)(596,798)(597,803)(598,804)(599,801)(600,802)(601,807)(602,808)(603,805)(604,806)(605,811)(606,812)(607,809)(608,810)(609,815)(610,816)(611,813)(612,814);;
s1 := (  3,  4)(  5, 65)(  6, 66)(  7, 68)(  8, 67)(  9, 61)( 10, 62)( 11, 64)( 12, 63)( 13, 57)( 14, 58)( 15, 60)( 16, 59)( 17, 53)( 18, 54)( 19, 56)( 20, 55)( 21, 49)( 22, 50)( 23, 52)( 24, 51)( 25, 45)( 26, 46)( 27, 48)( 28, 47)( 29, 41)( 30, 42)( 31, 44)( 32, 43)( 33, 37)( 34, 38)( 35, 40)( 36, 39)( 69,137)( 70,138)( 71,140)( 72,139)( 73,201)( 74,202)( 75,204)( 76,203)( 77,197)( 78,198)( 79,200)( 80,199)( 81,193)( 82,194)( 83,196)( 84,195)( 85,189)( 86,190)( 87,192)( 88,191)( 89,185)( 90,186)( 91,188)( 92,187)( 93,181)( 94,182)( 95,184)( 96,183)( 97,177)( 98,178)( 99,180)(100,179)(101,173)(102,174)(103,176)(104,175)(105,169)(106,170)(107,172)(108,171)(109,165)(110,166)(111,168)(112,167)(113,161)(114,162)(115,164)(116,163)(117,157)(118,158)(119,160)(120,159)(121,153)(122,154)(123,156)(124,155)(125,149)(126,150)(127,152)(128,151)(129,145)(130,146)(131,148)(132,147)(133,141)(134,142)(135,144)(136,143)(207,208)(209,269)(210,270)(211,272)(212,271)(213,265)(214,266)(215,268)(216,267)(217,261)(218,262)(219,264)(220,263)(221,257)(222,258)(223,260)(224,259)(225,253)(226,254)(227,256)(228,255)(229,249)(230,250)(231,252)(232,251)(233,245)(234,246)(235,248)(236,247)(237,241)(238,242)(239,244)(240,243)(273,341)(274,342)(275,344)(276,343)(277,405)(278,406)(279,408)(280,407)(281,401)(282,402)(283,404)(284,403)(285,397)(286,398)(287,400)(288,399)(289,393)(290,394)(291,396)(292,395)(293,389)(294,390)(295,392)(296,391)(297,385)(298,386)(299,388)(300,387)(301,381)(302,382)(303,384)(304,383)(305,377)(306,378)(307,380)(308,379)(309,373)(310,374)(311,376)(312,375)(313,369)(314,370)(315,372)(316,371)(317,365)(318,366)(319,368)(320,367)(321,361)(322,362)(323,364)(324,363)(325,357)(326,358)(327,360)(328,359)(329,353)(330,354)(331,356)(332,355)(333,349)(334,350)(335,352)(336,351)(337,345)(338,346)(339,348)(340,347)(409,613)(410,614)(411,616)(412,615)(413,677)(414,678)(415,680)(416,679)(417,673)(418,674)(419,676)(420,675)(421,669)(422,670)(423,672)(424,671)(425,665)(426,666)(427,668)(428,667)(429,661)(430,662)(431,664)(432,663)(433,657)(434,658)(435,660)(436,659)(437,653)(438,654)(439,656)(440,655)(441,649)(442,650)(443,652)(444,651)(445,645)(446,646)(447,648)(448,647)(449,641)(450,642)(451,644)(452,643)(453,637)(454,638)(455,640)(456,639)(457,633)(458,634)(459,636)(460,635)(461,629)(462,630)(463,632)(464,631)(465,625)(466,626)(467,628)(468,627)(469,621)(470,622)(471,624)(472,623)(473,617)(474,618)(475,620)(476,619)(477,749)(478,750)(479,752)(480,751)(481,813)(482,814)(483,816)(484,815)(485,809)(486,810)(487,812)(488,811)(489,805)(490,806)(491,808)(492,807)(493,801)(494,802)(495,804)(496,803)(497,797)(498,798)(499,800)(500,799)(501,793)(502,794)(503,796)(504,795)(505,789)(506,790)(507,792)(508,791)(509,785)(510,786)(511,788)(512,787)(513,781)(514,782)(515,784)(516,783)(517,777)(518,778)(519,780)(520,779)(521,773)(522,774)(523,776)(524,775)(525,769)(526,770)(527,772)(528,771)(529,765)(530,766)(531,768)(532,767)(533,761)(534,762)(535,764)(536,763)(537,757)(538,758)(539,760)(540,759)(541,753)(542,754)(543,756)(544,755)(545,681)(546,682)(547,684)(548,683)(549,745)(550,746)(551,748)(552,747)(553,741)(554,742)(555,744)(556,743)(557,737)(558,738)(559,740)(560,739)(561,733)(562,734)(563,736)(564,735)(565,729)(566,730)(567,732)(568,731)(569,725)(570,726)(571,728)(572,727)(573,721)(574,722)(575,724)(576,723)(577,717)(578,718)(579,720)(580,719)(581,713)(582,714)(583,716)(584,715)(585,709)(586,710)(587,712)(588,711)(589,705)(590,706)(591,708)(592,707)(593,701)(594,702)(595,704)(596,703)(597,697)(598,698)(599,700)(600,699)(601,693)(602,694)(603,696)(604,695)(605,689)(606,690)(607,692)(608,691)(609,685)(610,686)(611,688)(612,687);;
s2 := (  1,481)(  2,484)(  3,483)(  4,482)(  5,477)(  6,480)(  7,479)(  8,478)(  9,541)( 10,544)( 11,543)( 12,542)( 13,537)( 14,540)( 15,539)( 16,538)( 17,533)( 18,536)( 19,535)( 20,534)( 21,529)( 22,532)( 23,531)( 24,530)( 25,525)( 26,528)( 27,527)( 28,526)( 29,521)( 30,524)( 31,523)( 32,522)( 33,517)( 34,520)( 35,519)( 36,518)( 37,513)( 38,516)( 39,515)( 40,514)( 41,509)( 42,512)( 43,511)( 44,510)( 45,505)( 46,508)( 47,507)( 48,506)( 49,501)( 50,504)( 51,503)( 52,502)( 53,497)( 54,500)( 55,499)( 56,498)( 57,493)( 58,496)( 59,495)( 60,494)( 61,489)( 62,492)( 63,491)( 64,490)( 65,485)( 66,488)( 67,487)( 68,486)( 69,413)( 70,416)( 71,415)( 72,414)( 73,409)( 74,412)( 75,411)( 76,410)( 77,473)( 78,476)( 79,475)( 80,474)( 81,469)( 82,472)( 83,471)( 84,470)( 85,465)( 86,468)( 87,467)( 88,466)( 89,461)( 90,464)( 91,463)( 92,462)( 93,457)( 94,460)( 95,459)( 96,458)( 97,453)( 98,456)( 99,455)(100,454)(101,449)(102,452)(103,451)(104,450)(105,445)(106,448)(107,447)(108,446)(109,441)(110,444)(111,443)(112,442)(113,437)(114,440)(115,439)(116,438)(117,433)(118,436)(119,435)(120,434)(121,429)(122,432)(123,431)(124,430)(125,425)(126,428)(127,427)(128,426)(129,421)(130,424)(131,423)(132,422)(133,417)(134,420)(135,419)(136,418)(137,549)(138,552)(139,551)(140,550)(141,545)(142,548)(143,547)(144,546)(145,609)(146,612)(147,611)(148,610)(149,605)(150,608)(151,607)(152,606)(153,601)(154,604)(155,603)(156,602)(157,597)(158,600)(159,599)(160,598)(161,593)(162,596)(163,595)(164,594)(165,589)(166,592)(167,591)(168,590)(169,585)(170,588)(171,587)(172,586)(173,581)(174,584)(175,583)(176,582)(177,577)(178,580)(179,579)(180,578)(181,573)(182,576)(183,575)(184,574)(185,569)(186,572)(187,571)(188,570)(189,565)(190,568)(191,567)(192,566)(193,561)(194,564)(195,563)(196,562)(197,557)(198,560)(199,559)(200,558)(201,553)(202,556)(203,555)(204,554)(205,685)(206,688)(207,687)(208,686)(209,681)(210,684)(211,683)(212,682)(213,745)(214,748)(215,747)(216,746)(217,741)(218,744)(219,743)(220,742)(221,737)(222,740)(223,739)(224,738)(225,733)(226,736)(227,735)(228,734)(229,729)(230,732)(231,731)(232,730)(233,725)(234,728)(235,727)(236,726)(237,721)(238,724)(239,723)(240,722)(241,717)(242,720)(243,719)(244,718)(245,713)(246,716)(247,715)(248,714)(249,709)(250,712)(251,711)(252,710)(253,705)(254,708)(255,707)(256,706)(257,701)(258,704)(259,703)(260,702)(261,697)(262,700)(263,699)(264,698)(265,693)(266,696)(267,695)(268,694)(269,689)(270,692)(271,691)(272,690)(273,617)(274,620)(275,619)(276,618)(277,613)(278,616)(279,615)(280,614)(281,677)(282,680)(283,679)(284,678)(285,673)(286,676)(287,675)(288,674)(289,669)(290,672)(291,671)(292,670)(293,665)(294,668)(295,667)(296,666)(297,661)(298,664)(299,663)(300,662)(301,657)(302,660)(303,659)(304,658)(305,653)(306,656)(307,655)(308,654)(309,649)(310,652)(311,651)(312,650)(313,645)(314,648)(315,647)(316,646)(317,641)(318,644)(319,643)(320,642)(321,637)(322,640)(323,639)(324,638)(325,633)(326,636)(327,635)(328,634)(329,629)(330,632)(331,631)(332,630)(333,625)(334,628)(335,627)(336,626)(337,621)(338,624)(339,623)(340,622)(341,753)(342,756)(343,755)(344,754)(345,749)(346,752)(347,751)(348,750)(349,813)(350,816)(351,815)(352,814)(353,809)(354,812)(355,811)(356,810)(357,805)(358,808)(359,807)(360,806)(361,801)(362,804)(363,803)(364,802)(365,797)(366,800)(367,799)(368,798)(369,793)(370,796)(371,795)(372,794)(373,789)(374,792)(375,791)(376,790)(377,785)(378,788)(379,787)(380,786)(381,781)(382,784)(383,783)(384,782)(385,777)(386,780)(387,779)(388,778)(389,773)(390,776)(391,775)(392,774)(393,769)(394,772)(395,771)(396,770)(397,765)(398,768)(399,767)(400,766)(401,761)(402,764)(403,763)(404,762)(405,757)(406,760)(407,759)(408,758);;
poly := Group([s0,s1,s2]);;
 

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 

s0 := Sym(816)!(  1,207)(  2,208)(  3,205)(  4,206)(  5,211)(  6,212)(  7,209)(  8,210)(  9,215)( 10,216)( 11,213)( 12,214)( 13,219)( 14,220)( 15,217)( 16,218)( 17,223)( 18,224)( 19,221)( 20,222)( 21,227)( 22,228)( 23,225)( 24,226)( 25,231)( 26,232)( 27,229)( 28,230)( 29,235)( 30,236)( 31,233)( 32,234)( 33,239)( 34,240)( 35,237)( 36,238)( 37,243)( 38,244)( 39,241)( 40,242)( 41,247)( 42,248)( 43,245)( 44,246)( 45,251)( 46,252)( 47,249)( 48,250)( 49,255)( 50,256)( 51,253)( 52,254)( 53,259)( 54,260)( 55,257)( 56,258)( 57,263)( 58,264)( 59,261)( 60,262)( 61,267)( 62,268)( 63,265)( 64,266)( 65,271)( 66,272)( 67,269)( 68,270)( 69,275)( 70,276)( 71,273)( 72,274)( 73,279)( 74,280)( 75,277)( 76,278)( 77,283)( 78,284)( 79,281)( 80,282)( 81,287)( 82,288)( 83,285)( 84,286)( 85,291)( 86,292)( 87,289)( 88,290)( 89,295)( 90,296)( 91,293)( 92,294)( 93,299)( 94,300)( 95,297)( 96,298)( 97,303)( 98,304)( 99,301)(100,302)(101,307)(102,308)(103,305)(104,306)(105,311)(106,312)(107,309)(108,310)(109,315)(110,316)(111,313)(112,314)(113,319)(114,320)(115,317)(116,318)(117,323)(118,324)(119,321)(120,322)(121,327)(122,328)(123,325)(124,326)(125,331)(126,332)(127,329)(128,330)(129,335)(130,336)(131,333)(132,334)(133,339)(134,340)(135,337)(136,338)(137,343)(138,344)(139,341)(140,342)(141,347)(142,348)(143,345)(144,346)(145,351)(146,352)(147,349)(148,350)(149,355)(150,356)(151,353)(152,354)(153,359)(154,360)(155,357)(156,358)(157,363)(158,364)(159,361)(160,362)(161,367)(162,368)(163,365)(164,366)(165,371)(166,372)(167,369)(168,370)(169,375)(170,376)(171,373)(172,374)(173,379)(174,380)(175,377)(176,378)(177,383)(178,384)(179,381)(180,382)(181,387)(182,388)(183,385)(184,386)(185,391)(186,392)(187,389)(188,390)(189,395)(190,396)(191,393)(192,394)(193,399)(194,400)(195,397)(196,398)(197,403)(198,404)(199,401)(200,402)(201,407)(202,408)(203,405)(204,406)(409,615)(410,616)(411,613)(412,614)(413,619)(414,620)(415,617)(416,618)(417,623)(418,624)(419,621)(420,622)(421,627)(422,628)(423,625)(424,626)(425,631)(426,632)(427,629)(428,630)(429,635)(430,636)(431,633)(432,634)(433,639)(434,640)(435,637)(436,638)(437,643)(438,644)(439,641)(440,642)(441,647)(442,648)(443,645)(444,646)(445,651)(446,652)(447,649)(448,650)(449,655)(450,656)(451,653)(452,654)(453,659)(454,660)(455,657)(456,658)(457,663)(458,664)(459,661)(460,662)(461,667)(462,668)(463,665)(464,666)(465,671)(466,672)(467,669)(468,670)(469,675)(470,676)(471,673)(472,674)(473,679)(474,680)(475,677)(476,678)(477,683)(478,684)(479,681)(480,682)(481,687)(482,688)(483,685)(484,686)(485,691)(486,692)(487,689)(488,690)(489,695)(490,696)(491,693)(492,694)(493,699)(494,700)(495,697)(496,698)(497,703)(498,704)(499,701)(500,702)(501,707)(502,708)(503,705)(504,706)(505,711)(506,712)(507,709)(508,710)(509,715)(510,716)(511,713)(512,714)(513,719)(514,720)(515,717)(516,718)(517,723)(518,724)(519,721)(520,722)(521,727)(522,728)(523,725)(524,726)(525,731)(526,732)(527,729)(528,730)(529,735)(530,736)(531,733)(532,734)(533,739)(534,740)(535,737)(536,738)(537,743)(538,744)(539,741)(540,742)(541,747)(542,748)(543,745)(544,746)(545,751)(546,752)(547,749)(548,750)(549,755)(550,756)(551,753)(552,754)(553,759)(554,760)(555,757)(556,758)(557,763)(558,764)(559,761)(560,762)(561,767)(562,768)(563,765)(564,766)(565,771)(566,772)(567,769)(568,770)(569,775)(570,776)(571,773)(572,774)(573,779)(574,780)(575,777)(576,778)(577,783)(578,784)(579,781)(580,782)(581,787)(582,788)(583,785)(584,786)(585,791)(586,792)(587,789)(588,790)(589,795)(590,796)(591,793)(592,794)(593,799)(594,800)(595,797)(596,798)(597,803)(598,804)(599,801)(600,802)(601,807)(602,808)(603,805)(604,806)(605,811)(606,812)(607,809)(608,810)(609,815)(610,816)(611,813)(612,814);
s1 := Sym(816)!(  3,  4)(  5, 65)(  6, 66)(  7, 68)(  8, 67)(  9, 61)( 10, 62)( 11, 64)( 12, 63)( 13, 57)( 14, 58)( 15, 60)( 16, 59)( 17, 53)( 18, 54)( 19, 56)( 20, 55)( 21, 49)( 22, 50)( 23, 52)( 24, 51)( 25, 45)( 26, 46)( 27, 48)( 28, 47)( 29, 41)( 30, 42)( 31, 44)( 32, 43)( 33, 37)( 34, 38)( 35, 40)( 36, 39)( 69,137)( 70,138)( 71,140)( 72,139)( 73,201)( 74,202)( 75,204)( 76,203)( 77,197)( 78,198)( 79,200)( 80,199)( 81,193)( 82,194)( 83,196)( 84,195)( 85,189)( 86,190)( 87,192)( 88,191)( 89,185)( 90,186)( 91,188)( 92,187)( 93,181)( 94,182)( 95,184)( 96,183)( 97,177)( 98,178)( 99,180)(100,179)(101,173)(102,174)(103,176)(104,175)(105,169)(106,170)(107,172)(108,171)(109,165)(110,166)(111,168)(112,167)(113,161)(114,162)(115,164)(116,163)(117,157)(118,158)(119,160)(120,159)(121,153)(122,154)(123,156)(124,155)(125,149)(126,150)(127,152)(128,151)(129,145)(130,146)(131,148)(132,147)(133,141)(134,142)(135,144)(136,143)(207,208)(209,269)(210,270)(211,272)(212,271)(213,265)(214,266)(215,268)(216,267)(217,261)(218,262)(219,264)(220,263)(221,257)(222,258)(223,260)(224,259)(225,253)(226,254)(227,256)(228,255)(229,249)(230,250)(231,252)(232,251)(233,245)(234,246)(235,248)(236,247)(237,241)(238,242)(239,244)(240,243)(273,341)(274,342)(275,344)(276,343)(277,405)(278,406)(279,408)(280,407)(281,401)(282,402)(283,404)(284,403)(285,397)(286,398)(287,400)(288,399)(289,393)(290,394)(291,396)(292,395)(293,389)(294,390)(295,392)(296,391)(297,385)(298,386)(299,388)(300,387)(301,381)(302,382)(303,384)(304,383)(305,377)(306,378)(307,380)(308,379)(309,373)(310,374)(311,376)(312,375)(313,369)(314,370)(315,372)(316,371)(317,365)(318,366)(319,368)(320,367)(321,361)(322,362)(323,364)(324,363)(325,357)(326,358)(327,360)(328,359)(329,353)(330,354)(331,356)(332,355)(333,349)(334,350)(335,352)(336,351)(337,345)(338,346)(339,348)(340,347)(409,613)(410,614)(411,616)(412,615)(413,677)(414,678)(415,680)(416,679)(417,673)(418,674)(419,676)(420,675)(421,669)(422,670)(423,672)(424,671)(425,665)(426,666)(427,668)(428,667)(429,661)(430,662)(431,664)(432,663)(433,657)(434,658)(435,660)(436,659)(437,653)(438,654)(439,656)(440,655)(441,649)(442,650)(443,652)(444,651)(445,645)(446,646)(447,648)(448,647)(449,641)(450,642)(451,644)(452,643)(453,637)(454,638)(455,640)(456,639)(457,633)(458,634)(459,636)(460,635)(461,629)(462,630)(463,632)(464,631)(465,625)(466,626)(467,628)(468,627)(469,621)(470,622)(471,624)(472,623)(473,617)(474,618)(475,620)(476,619)(477,749)(478,750)(479,752)(480,751)(481,813)(482,814)(483,816)(484,815)(485,809)(486,810)(487,812)(488,811)(489,805)(490,806)(491,808)(492,807)(493,801)(494,802)(495,804)(496,803)(497,797)(498,798)(499,800)(500,799)(501,793)(502,794)(503,796)(504,795)(505,789)(506,790)(507,792)(508,791)(509,785)(510,786)(511,788)(512,787)(513,781)(514,782)(515,784)(516,783)(517,777)(518,778)(519,780)(520,779)(521,773)(522,774)(523,776)(524,775)(525,769)(526,770)(527,772)(528,771)(529,765)(530,766)(531,768)(532,767)(533,761)(534,762)(535,764)(536,763)(537,757)(538,758)(539,760)(540,759)(541,753)(542,754)(543,756)(544,755)(545,681)(546,682)(547,684)(548,683)(549,745)(550,746)(551,748)(552,747)(553,741)(554,742)(555,744)(556,743)(557,737)(558,738)(559,740)(560,739)(561,733)(562,734)(563,736)(564,735)(565,729)(566,730)(567,732)(568,731)(569,725)(570,726)(571,728)(572,727)(573,721)(574,722)(575,724)(576,723)(577,717)(578,718)(579,720)(580,719)(581,713)(582,714)(583,716)(584,715)(585,709)(586,710)(587,712)(588,711)(589,705)(590,706)(591,708)(592,707)(593,701)(594,702)(595,704)(596,703)(597,697)(598,698)(599,700)(600,699)(601,693)(602,694)(603,696)(604,695)(605,689)(606,690)(607,692)(608,691)(609,685)(610,686)(611,688)(612,687);
s2 := Sym(816)!(  1,481)(  2,484)(  3,483)(  4,482)(  5,477)(  6,480)(  7,479)(  8,478)(  9,541)( 10,544)( 11,543)( 12,542)( 13,537)( 14,540)( 15,539)( 16,538)( 17,533)( 18,536)( 19,535)( 20,534)( 21,529)( 22,532)( 23,531)( 24,530)( 25,525)( 26,528)( 27,527)( 28,526)( 29,521)( 30,524)( 31,523)( 32,522)( 33,517)( 34,520)( 35,519)( 36,518)( 37,513)( 38,516)( 39,515)( 40,514)( 41,509)( 42,512)( 43,511)( 44,510)( 45,505)( 46,508)( 47,507)( 48,506)( 49,501)( 50,504)( 51,503)( 52,502)( 53,497)( 54,500)( 55,499)( 56,498)( 57,493)( 58,496)( 59,495)( 60,494)( 61,489)( 62,492)( 63,491)( 64,490)( 65,485)( 66,488)( 67,487)( 68,486)( 69,413)( 70,416)( 71,415)( 72,414)( 73,409)( 74,412)( 75,411)( 76,410)( 77,473)( 78,476)( 79,475)( 80,474)( 81,469)( 82,472)( 83,471)( 84,470)( 85,465)( 86,468)( 87,467)( 88,466)( 89,461)( 90,464)( 91,463)( 92,462)( 93,457)( 94,460)( 95,459)( 96,458)( 97,453)( 98,456)( 99,455)(100,454)(101,449)(102,452)(103,451)(104,450)(105,445)(106,448)(107,447)(108,446)(109,441)(110,444)(111,443)(112,442)(113,437)(114,440)(115,439)(116,438)(117,433)(118,436)(119,435)(120,434)(121,429)(122,432)(123,431)(124,430)(125,425)(126,428)(127,427)(128,426)(129,421)(130,424)(131,423)(132,422)(133,417)(134,420)(135,419)(136,418)(137,549)(138,552)(139,551)(140,550)(141,545)(142,548)(143,547)(144,546)(145,609)(146,612)(147,611)(148,610)(149,605)(150,608)(151,607)(152,606)(153,601)(154,604)(155,603)(156,602)(157,597)(158,600)(159,599)(160,598)(161,593)(162,596)(163,595)(164,594)(165,589)(166,592)(167,591)(168,590)(169,585)(170,588)(171,587)(172,586)(173,581)(174,584)(175,583)(176,582)(177,577)(178,580)(179,579)(180,578)(181,573)(182,576)(183,575)(184,574)(185,569)(186,572)(187,571)(188,570)(189,565)(190,568)(191,567)(192,566)(193,561)(194,564)(195,563)(196,562)(197,557)(198,560)(199,559)(200,558)(201,553)(202,556)(203,555)(204,554)(205,685)(206,688)(207,687)(208,686)(209,681)(210,684)(211,683)(212,682)(213,745)(214,748)(215,747)(216,746)(217,741)(218,744)(219,743)(220,742)(221,737)(222,740)(223,739)(224,738)(225,733)(226,736)(227,735)(228,734)(229,729)(230,732)(231,731)(232,730)(233,725)(234,728)(235,727)(236,726)(237,721)(238,724)(239,723)(240,722)(241,717)(242,720)(243,719)(244,718)(245,713)(246,716)(247,715)(248,714)(249,709)(250,712)(251,711)(252,710)(253,705)(254,708)(255,707)(256,706)(257,701)(258,704)(259,703)(260,702)(261,697)(262,700)(263,699)(264,698)(265,693)(266,696)(267,695)(268,694)(269,689)(270,692)(271,691)(272,690)(273,617)(274,620)(275,619)(276,618)(277,613)(278,616)(279,615)(280,614)(281,677)(282,680)(283,679)(284,678)(285,673)(286,676)(287,675)(288,674)(289,669)(290,672)(291,671)(292,670)(293,665)(294,668)(295,667)(296,666)(297,661)(298,664)(299,663)(300,662)(301,657)(302,660)(303,659)(304,658)(305,653)(306,656)(307,655)(308,654)(309,649)(310,652)(311,651)(312,650)(313,645)(314,648)(315,647)(316,646)(317,641)(318,644)(319,643)(320,642)(321,637)(322,640)(323,639)(324,638)(325,633)(326,636)(327,635)(328,634)(329,629)(330,632)(331,631)(332,630)(333,625)(334,628)(335,627)(336,626)(337,621)(338,624)(339,623)(340,622)(341,753)(342,756)(343,755)(344,754)(345,749)(346,752)(347,751)(348,750)(349,813)(350,816)(351,815)(352,814)(353,809)(354,812)(355,811)(356,810)(357,805)(358,808)(359,807)(360,806)(361,801)(362,804)(363,803)(364,802)(365,797)(366,800)(367,799)(368,798)(369,793)(370,796)(371,795)(372,794)(373,789)(374,792)(375,791)(376,790)(377,785)(378,788)(379,787)(380,786)(381,781)(382,784)(383,783)(384,782)(385,777)(386,780)(387,779)(388,778)(389,773)(390,776)(391,775)(392,774)(393,769)(394,772)(395,771)(396,770)(397,765)(398,768)(399,767)(400,766)(401,761)(402,764)(403,763)(404,762)(405,757)(406,760)(407,759)(408,758);
poly := sub<Sym(816)|s0,s1,s2>;
 

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

Twisty Puzzle